Modeling Hierarchical System with Operads

TL;DR

This paper introduces a novel hierarchical modeling approach for complex systems using operads and functorial semantics, demonstrated through a high-precision measurement system, enabling detailed failure diagnosis and probabilistic analysis.

Contribution

It develops a new operad-based framework for modeling and analyzing failure modes in complex systems, integrating combinatorial structures with probabilistic semantics.

Findings

Operad-based models effectively represent hierarchical system interactions.

Functorial semantics organize failure probabilities systematically.

The approach extends to specific failure modes for detailed diagnosis.

Abstract

This paper applies operads and functorial semantics to address the problem of failure diagnosis in complex systems. We start with a concrete example, developing a hierarchical interaction model for the Length Scale Interferometer, a high-precision measurement system operated by the US National Institute of Standards and Technology. The model is expressed in terms of combinatorial/diagrammatic structures called port-graphs, and we explain how to extract an operad LSI from a collection of these diagrams. Next we show how functors to the operad of probabilities organize and constrain the relative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.